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2 years ago

What is a situation in which a polynomial model might make sense, and why?

Mathematics

1 answer:

ololo11 [35]2 years ago

7 0

Answer and Step-by-step explanation:

Polynomial models are an excellent implementation for determining which input element reaction and their direction. These are also the most common models used for the scanning of designed experiments. It defines as:

Z = a0 + a1x1 + a2x2 + a11x12 + a22x22+ a12x1x2 + Є

It is a quadratic (second-order) polynomial model for two variables.

The single x terms are the main effect. The squared terms are quadratic effects. These are used to model curvature in the response surface. The product terms are used to model the interaction between explanatory variables where Є is an unobserved random error.

A polynomial term, quadratic or cubic, turns the linear regression model into a curve. Because x is squared or cubed, but the beta coefficient is a linear model.

In general, we can model the expected value of y as nth order polynomial, the general polynomial model is:

Y = B0 + B1x1 + B2x2 + B3x3 + … +

These models are all linear since the function is linear in terms of the new perimeter. Therefore least-squares analysis, polynomial regression can be addressed entirely using multiple regression

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An airplane has its auto pilot set to fly in a direction of 40 degrees at a speed of 320 mph. The wind is blowing the airplane t

Effectus [21]

Answer:

distance: 320.624 miles

direction: 43.576°

Step-by-step explanation:

The speed and direction can be found by adding the given vectors.

... 320∠40° + 20∠130°

... = (320·cos(40°), 320·sin(40°)) + (20·cos(130°), 20·sin(130°))

... = (245.134, 205.692) +(-12.856, 15.321) = (232.278, 221.013)

The magnitude of the vector with these components is found using the Pythagorean theorem. The direction is found using the arctangent function.

... = √(232.278² +221.013²)∠arctan(221.013/232.278)

... = 320.624∠43.576°

_____

A suitable vector or graphing calculator can do this easily. In the screenshot of a TI-84 app below, the variable D has the value π/180. The display mode is set to degrees.

_____

Comment on coordinate systems

Navigation directions are generally measured clockwise from North. Angles in the usual x-y coordinate plane are measured counterclockwise from +x (effectively, East). You can consider the geometry of the navigation coordinate system to be a reflection across the line y=x of the geometry of the usual x-y coordinate system.

Reflection does not change lengths or angles within a given geometry. Hence, we can use all the usual tools of vector calculation using navigation coordinates, without bothering to translate them back and forth to x-y coordinates.

_____

Problems like this generally can be worked using the Law of Cosines and the Law of Sines, too. It generally helps to draw a diagram so you can find the values of the angles betwee the various vectors more easily.

8 0

2 years ago

Given the median 24 and trapezoid MNOP what is the value of x

masha68 [24]

1. Given the bases a and b of a trapezoid, the length of the median m can be found by the formula $m= \frac{a+b}{2}$

2. MP and NO are the bases so applying the above formula:

$24= \frac{(x+8)+(5x+4)}{2}$

$48= 6x+12$

$6x=36$

x=6

Check the picture for the proof of the theorem m=(a+b)/2

8 0

2 years ago

Read 2 more answers

The 8th term of a GP is -7/32 find its common ratio if its first term is 28

Ugo [173]

<h2>Common ratio = -1/2</h2>

Step-by-step explanation:

$\text{8}^{th}$ term of a Geometric progression is given as $\dfrac{-7}{32}$ . The first term is given as $28$ .

Any general Geometric progression can be represented using the series $a,ar,ar^{2},ar^{3},ar^{4}...\text{ }ar^{n-1}$ .

The first term in such a GP is given by $a$ , common ratio by $r$ , and the $n^{th}$ term is given by $ar^{n-1}$ .

In the given GP, $a=28;t_{8}=ar^{7}=\dfrac{-7}{32}\\\\28r^{7}=\dfrac{-7}{32}\\\\r^{7}=\dfrac{-1}{128}\\\\r=\dfrac{-1}{2}$

∴ Common ratio is $\dfrac{-1}{2}$ .

5 0

2 years ago

"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r

sergiy2304 [10]

Answer:

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

Let $p_1$ = proportion of drivers that were in compliance initially

$p_2$ = proportion of drivers that were in compliance one year later

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$ {means that there is not any statistical difference in these two proportions measured initially and then one year later}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{ \frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of drivers in compliance initially = 98.9%

$\hat p_2$ = sample proportion of drivers in compliance one year later = 96.9%

$n_1$ = sample of drivers initially = 1,250

$n_2$ = sample of drivers one year later = 1,100

(b) So, the test statistics = $\frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }$

= 3.33

Now, P-value of the test statistics is given by;

P-value = P(Z > 3.33) = 1 - P(Z $\leq$ 3.33)

= 1 - 0.99957 = 0.00043

Since in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

Since our test statistics does not lies within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

7 0

2 years ago

Choose the function whose graph is given by:

katen-ka-za [31]

Answer:

D. $y=\tan (x-\pi)+2$